Sylow p-subgroup

If (G,*) is a group then any subgroupMathworldPlanetmathPlanetmath of order pa for any integer a is called a p-subgroupPlanetmathPlanetmath. If |G|=pam, where pm then any subgroup S of G with |S|=pa is a Sylow p-subgroup. We use Sylp(G) for the set of Sylow p-groupsMathworldPlanetmath of G.

More generally, if G is any group (not necessarily finite), a Sylow p-subgroup is a maximal p-subgroup of G.

Title Sylow p-subgroup
Canonical name SylowPsubgroup
Date of creation 2013-03-22 12:50:59
Last modified on 2013-03-22 12:50:59
Owner Henry (455)
Last modified by Henry (455)
Numerical id 8
Author Henry (455)
Entry type Definition
Classification msc 20D20
Synonym Sylow subgroup
Synonym Sylow group
Related topic SylowTheorems
Related topic ProofOfSylowTheorems
Related topic PPrimaryComponent
Related topic SylowsThirdTheorem
Defines Sylow p-subgroup
Defines p-subgroup